A solution has a 1 : 4 mole ratio of pentane to hexane. The vapour pressures of the pure hydrocarbons at 20^ C are 440 mm Hg for pentane and 120 ~mm Hg for hexane. the mole fraction of pentane in the vapour phase would be:

Step-by-step solution

aligned n_ C ₅ H ₁₂ n_ C ₆ H ₁₄ & = 1 4 X _ C ₃ H ₁₂ & = 1 5 and X _ C ₆ H ₁₄ = 4 5 P _ C ₅ H ₁₂ ^ & =440 ~mm Hg ; P _ C ₆ H ₁₄ ^ & =120 ~mm Hg P _ T & = P _ C ₅ H ₁₂ ^ X _ C ₅ H ₁₂ & + P _ C ₆ H ₁₄ ^ X _ C ₆ H ₁₄ & =440 1 5 +120 4 5 & =184 ~mm of Hg aligned By Raoult's Law, P _ C ₅ H ₁₂ = P _ C ₅ H ₁₂ ^ X _ C ₅ H ₁₂ By Dalton's Law, P _ C ₅ H ₁₂ = X _ C ₅ H ₁₂ ^ P From (1) and (2), aligned P _ C ₅ H ₁₂ & =440 1 5 =88 ~mm of Hg 88 & = X _ C ₅ H ₁₂ ^ 184 X ^ & = 88 184 ; X ^ =0.478 . aligned